Let 
. Three distinct points P. Q and R are randomly chosen from X. Then the probability that P, Q and R form a triangle whose area is a positive integer, is
Text Solution
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Solving corresponding equations
X = {(1,1), (1,0), (1-1), (1,2), (1-2), (2, 3), (2,2), (2,1), (2,0), (2-1), (2-2), (2-3)}
Let S be the sample space & E be the event n(S) = 12 C 3
For E
Selecting 3 points in which 2 points are either or x=l & x = 2 but distance b/w then is even Triangles with base 2 :
= 3x7 + 5x5 = 46
Triangles with base 4 :
= 1x7 + 3x5 = 22
Triangles with base 6 :
= 1x5 = 5
Ans.
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